Dynamics of correlations in the stock market

  • S. Drożdż
  • F. Grümmer
  • F. Ruf
  • J. Speth


Financial empirical correlation matrices of all the companies which both, the Deutsche Aktienindex (DAX) and the Dow Jones comprised during the time period 1990–1999 are studied using a time window of a limited, either 30 or 60, number of trading days. This allows a clear identification of the resulting correlations. On both these markets the decreases turn out to be always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix, while increases are more competitive and thus less collective. Generically, however, the remaining eigenstates of the correlation matrix are, on average, consistent with predictions of the random matrix theory. Effects connected with the world globalization are also discussed and a leading role of the Dow Jones is quantified. This effect is particularly spectacular during the last few years, and it turns out to be crucial to properly account for the time-zone delays in order to identify it.


Stock Market Correlation Matrix Large Eigenvalue Collective State Localization Length 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Drożdż S, Ruf F, Speth J, Wójcik M (1999) Imprints of log-periodic selfsimilarity in the stock market. Eur. Phys. J. B 10:589ADSCrossRefGoogle Scholar
  2. 2.
    Drożdż S, Grümmer F, Górski A, Ruf F, Speth J (2000) Dynamics of competition between collectivity and noise in the stock market. Physica A 287:440ADSCrossRefGoogle Scholar
  3. 3.
    Elton EJ, Gruber MJ (1995) Modern Portfolio Theory and Investment Analysis. Wiley J and Sons, New YorkGoogle Scholar
  4. 4.
    Izrailev FM (1990) Simple models of quantum chaos: spectrum and eigenfunctions. Phys. Rep. 196:299MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    Laloux L, Cizeau P, Bouchaud J-P, Potters M (1999) Noise dressing of financial correlation matrices. Phys. Rev. Lett. 83:1467ADSCrossRefGoogle Scholar
  6. 6.
    Markowitz H, (1959) Portfolio Selection: Efficient Diversification of Investments. Wiley J and Sons, New YorkGoogle Scholar
  7. 7.
    Mehta ML (1991) Random Matrices. Academic Press, BostonMATHGoogle Scholar
  8. 8.
    Plerou V, Gopikrishnan P, Rosenow B, Amaral LAN, Stanley HE (1999) Universal and nonuniversal properties of cross-correlations in financial time-series. Phys. Rev. Lett. 83:1471ADSCrossRefGoogle Scholar
  9. 9.
    Sengupta AM, Mitra PP (1999) Distribution of singular values for some random matrices. Phys. Rev. E60:3389ADSCrossRefGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • S. Drożdż
    • 1
    • 2
  • F. Grümmer
    • 1
  • F. Ruf
    • 3
  • J. Speth
    • 1
  1. 1.Institut für KernphysikForschungszentrum JülichJülichGermany
  2. 2.Institute of Nuclear PhysicsKrakówPoland
  3. 3.WestLB International S.A.Charl.Luxembourg

Personalised recommendations